PYQs Based Test - 23 : Cauchy's Integral Theorem and Formula

Topics Covered

Sample Questions from this Test

1. Let $f(z)=\frac{1}{z^2+6z+9}$ defined in the complex plane. The integral ∮${}_c$ f(z)dz over the contour of a circle c with center at the origin and unit radius is ___.
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2. The closed loop line integral _≤ft| z | = 5^ {z^3 + z^2 + 8}z + 2dz evaluated counter-clockwise, is
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3. The value of the contour integral in the complex plane
   
   $\oint \frac{z^3-2z+3}{z-2}dz$
   
   along the contour |z| = 3, taken counterclockwise is
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Test Instructions

• The test contains 10 questions and a total of 16 marks.
• You will have 180 minutes to complete the test. The timer cannot be paused once started.
• Negative marking: 0.25 mark(s) deducted per wrong answer.
• Use the question palette to mark questions for review and navigate freely.
• Detailed solutions and analytics are available immediately after submission.
• This is a free practice test. No login required to attempt.